Eating the flesh of pigs is forbidden in Islam as it is ordered in the Quran. Allah Almighty says, [ Forbidden to you (for food) are carrion, blood, swine flesh, and that which has been dedicated to any other than Allah; that which has been strangled; that which has been beaten to death (by a blunt instrument); that which fell (a long fall); that which was gored by horns; that of which predators have eaten—saving that which you make lawful (by slaughtering before they die); and which has been sacrificed to idols.] (Al-Maidah: 3)
Therefore, we have to abstain from consuming its flesh as well as any food that is fried in its oil, since pork is impure, and hence, it contaminates the oil in which it is fried.
In his response to your question, Sheikh Abdul-Majeed Subh, a prominent Azharite scholar, stated:
Almighty Allah says in the Quran, [Say: I do not find in that which has been revealed to me anything forbidden for an eater to eat of except that it be what has died of itself, or blood poured forth, or flesh of swine-- for that surely is unclean-- or that which is a transgression, other than (the name of) Allah having been invoked on it; but whoever is driven to necessity, not desiring nor exceeding the limit, then surely your Lord is Forgiving, Merciful.] (Al-An`am 6:145)
Therefore, some scholars say that only the flesh of the swine is impure, so eating food that has been fried in the same oil in which pork has been fried, is permissible. The justification here is that Almighty Allah only mentioned its flesh as being forbidden in the verse.
However, the majority of scholars are of the opinion that the entire body of the pig is forbidden; its flesh, bones, and fat. Therefore, we have to avoid eating any food that has been fried in the same oil in which pork has been fried.
Sheikh Ahmad Kutty, senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Canada, added,
We are not allowed to eat food that has been fried in the same oil in which pork or its by-products have been fried. It is clearly haram and we must not rationalize it. Therefore, stay away from it as best as you can.